Problem: Simplify the following expression: $z = \dfrac{36y}{-16y + 44}$ You can assume $y \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $36y = (2\cdot2\cdot3\cdot3 \cdot y)$ The denominator can be factored: $-16y + 44 = - (2\cdot2\cdot2\cdot2 \cdot y) + (2\cdot2\cdot11)$ The greatest common factor of all the terms is $4$ Factoring out $4$ gives us: $z = \dfrac{(4)(9y)}{(4)(-4y + 11)}$ Dividing both the numerator and denominator by $4$ gives: $z = \dfrac{9y}{-4y + 11}$